Question

Simplify the expression (it'll be below this):

Answer 1

\[\sqrt[5]{x ^{8}}\]

Answer 2

a. \[x^{4}\]

b. \[x^{8}\]

c. \[x^{5}\sqrt{x ^{3}}\]

d. \[x^{3}\sqrt[5]{x}\]

Answer 3

and x^8 means x*x*x*x*x*x*x*x (8 x's multiplied together)

Answer 4

the 5th root means you can "take out" 5 x's multiplied together, and replace them with one x on the outside of the fifth root sign.

Answer 5

fixed typo (I meant one x on the outside)

Answer 6

Sorry I don't really understand what any of that means.

Answer 7

do you get this part
x^8 means x*x*x*x*x*x*x*x (8 x's multiplied together)

Answer 8

Yes I know what x^8 means.

Answer 9

Here, we are taking the fifth root of x^8. This can be rewritten by raising x^8 to the power of 1/5, in the same way that if we take the square root of a value it is the same as raising that value to the power of 1/2. The Laws of Indices states that (x^a)^b = x^ab, so (x^8)^1/5 = x^8/5. Unless I'm missing something, I can't see any of the above answers matching up with this, as if we used the same method on (c.) and (d.) we would get x^5/3 and x^3/5 respectively.

Answer 10

if you take the 5th root of 5 x's like this
\[ \sqrt[5]{x\cdot x\cdot x\cdot x\cdot x}\]
that simplifies to x
\[ \sqrt[5]{x\cdot x\cdot x\cdot x\cdot x} = x\]